Möbius 变换：球面投影的 MD 圆

GeoGebra 命令及参数

1. Sequence((r * cos(t)) + x(O) + ((y(O) + (r * sin(t))) * ί), t, -3.14159, π, (2 * π / n)) → z_*
2. Zip(fz(z), z, z_*) → fz_1
3. Sequence((x(Element[fz_1, k]), y(Element[fz_1, k]), ht), k, 1, n) → fz_*
4. CurveCartesian((r * cos(t)), (r * sin(t)), ht, t, 0, 6.283185307179586) → d_1
5. Vector(z_#, f_{(z#.)}) → w
6. Textfield(f_{(z#)}) → inputBox2
7. CurveCartesian(t, 0, ht, t, -5, 5) → Xh
8. CurveCartesian(0, t, ht, t, -5, 5) → Yh
9. Textfield(z_*) → inputBox3
10. Intersect(xAxis, yAxis) → B
11. Sphere(A, B) → f
12. Vector(C, z_#) → u
13. Ray(C, z_#) → g
14. Intersect(g, f) → D, E
15. Sphere(F, G) → h
16. Intersect(zAxis, h, 1) → H
17. Vector(f_{(z#.)}, H) → v
18. Ray(f_{(z#.)}, H) → i
19. Intersect(i, h) → I, J
20. Textfield(Fz) → inputBox1
21. Sequence(Vector[Element[fz_*, j], (0, 0, -5)], j, 1, n) → ProjVectfz_*
22. Sequence(Vector[(0, 0, 2), Element[z_*, j]], j, 1, n) → ProjVectz_*
23. Sequence(Intersect[Ray[Element[fz_*, j], (0, 0, -5)], h], j, 1, n) → Projfz_*
24. Sequence(Intersect[Line[Element[z_*, j], (0, 0, 2)], f], j, 1, n) → Projz_*
25. Sequence(Vector[Element[z_*, j], Element[fz_*, j]], j, 1, n) → fvec_*
26. Vector(f_{(z#.)}, H) → k
27. Point(C_O) → K
28. Locus(PfzK, K) → loc1